Several boxes of apples are undergoing a quality check. What will be the easiest way to do it? Checking all the apples piece by piece will be time-consuming.

Taking a few apples from each box to examine is the most convenient way. This process is called sampling. The number of all the apples in every box is the population. The population is defined to be the set of people, objects, measurements or events.

A sample is a method of survey that takes a representative of the population. It is the subset of the population. The concept of having a representative leads to random sampling.

Random SamplingRandom sampling is a method that, in a population, every element has a chance to be included in a sample. The element takes randomly without a purpose. It gives equal opportunity for the population to be selected.

Example:You want to know the usual number of children in your classmates’ families. Which of the following is a good representative of the class?
a. A sample consisting of your friends.
b. A sample consisting all of your classmate’s names drawn from a box.

The answer is b. Choosing your friends may lead to the wrong conclusion. This sample will not represent the correct number of children in your classmates families. Sample b supports the idea of random sampling so everyone has a chance to be included.

Stratified SamplingStratified sampling is when the population can be classified into groups or strata. The population consist of different ages, race and gender. The representative for each group must be proportional to the size of the layer.
\( Size \ of \ each \ groups \ = \frac{size \ of \ whole \ sample}{size \ of \ population} \times \ size \ of \ layer\)

This way, we can look at what the ratio of the whole population we need is and for each layer.
Example:You want to know how many people in a population of 500 watch opera. To make the survey accurate, you will need to classify the population into different layers or subgroup. In the population, we will have 50 representatives.
In each age group, we will have:
20 – below = \(\frac{ 50}{500}\times 90\) =9
21 – 30 =\(\frac{50}{500}\times 180\) =18
31 – 40 = \( \frac{50}{500}\times 50\) =5
41 – 50 = \(\frac{50}{500}\times 100\) =10
51 – Above = \(\frac{50}{500}\times 80\) = 8

Discrete and Continuous MeasuresDifferent sampling methods such as random or stratified need representatives. There are two types of variables: discrete and continuous.

Discrete VariablesA discrete variable is countable in a finite amount of time. For example, you can count the money in your wallet, the number of girls in your class, or the number of people in a van.

Example:The number of people in a van can be any whole number from 1 to 18. It is impossible to have a fraction or decimals. We cannot have a half of person.

Continuous VariablesA continuous variable can be any value in a range. It cannot be counted as it approaches infinity.

Example:Time can be years, months, days, hours, minutes, seconds, milliseconds and so on as time continues. It can be a discrete variable if we have counted in years.